Finite element analysis (FEA) is the process of creating a finite element mesh (“FEM”), which represents a physical domain upon which some physical phenomenon is to be analyzed. These domains can be broken up into either two dimensional (“2D”) or three dimensional (“3D”) domains. 3D domains represent the full-3D dimensions of an actual 3D domain. 3D domains are most often modeled with either tetrahedral or hexahedral elements. Less often, 3D domains are modeled with pyramid or wedge elements. FIG. 1 illustrates these four basic element types.
2D domains represent a physical phenomenon which is geometrically located in some kind of surface (either planar or non-planar), such as surface wave front propagation in liquids, or a thin sheet metal object such as the hood of a car. In addition, 2D domains are used to represent a simplification of a 3D domain, such as a cross-section of a 3D domain. 2D domains are most often modeled with either quadrilateral or triangular elements. FIG. 2 illustrates these 2D element types.
FEMs are typically composed of a single element type. For example, a hexahedral mesh is composed of only hexahedral elements. A “hybrid” mesh is a mesh composed of more than a single element type. For most FEA solvers, a non-hybrid mesh is preferred. Many FEA solvers do not support hybrid meshes.
During the process of FEA, it may become necessary to modify the density of mesh elements in a local region of a mesh in order to better adapt the mesh to the physics being modeled in the analysis. Refinement is the process of adding elements to the mesh. Coarsening is the process of removing elements from the mesh. There are many types of refinement and coarsening. However, for many applications, the most applicable types of refinement and coarsening are those that (1) are conformal, (2) are localized, (3) maintain the original mesh element type (i.e. non-hybrid), and (4) are independent of prior refinements.